Application of complex codes to miximize feeder link utilization

ABSTRACT

A method of increasing utilization of user link bandwidth for a code division multiple access communications system is disclosed that includes the steps of selecting a set of orthogonal complex codes each having a code length that is greater than a code length of an optimum real code and less than or equal to a number of antenna elements in an antenna array of the feeder link.

BACKGROUND OF THE INVENTION

[0001] The present invention relates generally to code division multipleaccess (CDMA) cellular communications systems. More specifically, butwithout limitation thereto, the present invention relates to assigningvariable length codes to service a maximum number of users in a codedivision multiple access service area that is assigned a fixed frequencyband.

[0002] The radio frequency spectrum is limited almost everywhere in theworld and is generally licensed in fixed frequency bands. Code divisionmultiple access (CDMA) cellular communications systems typically use aset of CDMA codes that are orthogonal to one another to avoid mutualinterference. The term orthogonal is applied to a set of codes if thevector dot product of any code in the set with any other code in the setresults in zero. For example, the code (−1, −1) is orthogonal to thecode (−1, 1) since −1*−1+−1*1=0. Currently known orthogonal CDMA codeshave a code length of 2^(n), where n is a positive integer. For example,if each antenna element receives a signal having a bandwidth of 5 MHzand the available bandwidth for the feeder link is 500 Mhz, then theratio of total available feeder link bandwidth to element bandwidth is100, which is not a power of 2. In this example, the parameters ofavailable feeder link bandwidth and antenna element bandwidth aredifficult to change. The element bandwidth is dictated by the thirdgeneration wireless standards, and the feeder link bandwidth is assignedby a regulatory agency such as the Federal Communications Commission.Using conventional CDMA codes, the longest code length that could beused in this example is 64. The resulting feeder link bandwidth wouldtherefore be 320 MHz, resulting in an unused bandwidth of 180 MHz. Theunused bandwidth represents a loss of revenue from potential CDMAsubscribers that might otherwise be included in the same service area.

SUMMARY OF THE INVENTION

[0003] The present invention advantageously addresses the problems aboveas well as other problems by providing a method of increasingutilization of feeder link bandwidth for a code division multiple accesscommunications system.

[0004] In one embodiment, the present invention may be characterized amethod of increasing utilization of feeder link bandwidth for a codedivision multiple access communications system that includes the stepsof selecting a set of orthogonal complex codes each having a code lengththat is greater than a code length of an optimum real code and less thanor equal to a number of antenna elements in an antenna array of a feederlink; and transferring symbols via the feeder link wherein each symbolis represented by a corresponding one of the set of orthogonal complexcodes.

[0005] In another embodiment, the present invention may be characterizedas a code division multiple access communications system that includes abase station; a geo-stationary platform; a feeder link coupled to thebase station and the geo-stationary platform for transferring symbolsbetween the base station and the geo-stationary platform; a plurality ofuser terminals; and at least one feeder link coupled respectively to theplurality of user terminals and to the geo-stationary platform fortransferring symbols between the geo-stationary platform and at leastone of the plurality of user terminals wherein each symbol isrepresented by a corresponding one of a set of orthogonal complex codeshaving a code length that is greater than a code length of an optimumreal code and less than or equal to a number of antenna elements of anantenna array of a feeder link.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The features and advantages of the present invention may beapprehended from the following description thereof, presented inconjunction with the following drawings wherein:

[0007]FIG. 1 is a diagram of a code division multiple access (CDMA)communications system of the prior art; and

[0008]FIG. 2 is an exemplary set of orthogonal complex codes for themaximizing the user link bandwidth of the code division multiple accesscommunications system of FIG. 1 according to an embodiment of thepresent invention.

[0009] Corresponding reference characters indicate correspondingelements throughout the several views of the drawings.

DESCRIPTION OF THE EMBODIMENTS

[0010]FIG. 1 is a diagram of a typical code division multiple access(CDMA) communications system 100. Shown in FIG. 1 are a base station102, a feeder link 104, a geo-stationary platform 106, user links 108,and user terminals 110.

[0011] The base station 102 transmits and receives symbols between userterminals 110 across the feeder link 104. The feeder link 104 is an RFcommunications link between the base station 102 and the geo-stationaryplatform 106. The geo-stationary platform 106 is typically ageo-stationary satellite, however other platforms having a relativelyfixed position with respect to the base station 102 may also be usedaccording to techniques well known in the art. Because the feeder link104 is between only two points (point-to-point), code division multipleaccess communications between the base station 102 and thegeo-stationary satellite 106 are generally synchronous, and may bemodulated by, for example, quadrature phase shift keying (QPSK).

[0012] The user terminals 110, may be, for example, cellular telephones.The user links 108 are RF communications links between the respectiveuser terminals 110 and the geo-stationary satellite 106. Because theuser links 108 are between multiple points whose positions relative tothe geo-stationary satellite 106 may change (point-to-multiple-point),communications between the user terminals 110 and the geo-stationarysatellite 106 are generally asynchronous, and may be modulated, forexample, by quadrature phase shift keying (QPSK).

[0013] For the feeder link application, the variables are the number ofantenna elements in a phased array antenna selected for a given antennaarray gain and beamwidth.

[0014] To avoid mutual interference, code division multiple access(CDMA) communications systems generally use mutually orthogonal codesfor transferring symbols across the user links 108. One example ofmutually orthogonal codes is a set of Walsh codes. Walsh codes may begenerated from Walsh code functions as follows. To generate a Walsh codesequence of code length two starting from a seed value of −1 for a Walshcode of code length one, the seed value of −1 is appended to itself togenerate the first Walsh code, (−1,−1). The bit-inverse of the seedvalue is appended to the seed value to generate the second Walsh code,(−1,1). This is the equivalent of creating the 2-bit Walsh code tableshown in Table 1 below. TABLE 1 Walsh Code W0 W1 0 −1 −1 1 −1 1

[0015] The procedure used to create Table 1 may be repeated to generatethe Walsh codes for the next higher order, i.e., the next longer Walshcode length, as shown in Table 2 below. The 2×2 matrix in bit positionsW0 and W1, also called the Hadamard transform matrix, is appended toitself in bit positions W2 and W3 to generate the first two Walsh codes0 and 1. The second two Walsh codes 2 and 3 are generated by appendingthe bit-inverse of the 2×2 matrix to the original 2×2 matrix. TABLE 2Walsh Code W0 W1 W2 W3 0 −1 −1 −1 −1 1 −1 1 −1 1 2 −1 −1 1 1 3 −1 1 1 −1

[0016] Additional Walsh code tables for the higher order Walsh codelengths may be generated by repeating the procedure above. For example,to create eight-bit Walsh codes, the 4×4 matrix of Table 2 is replicatedthree times and inverted in the lower right hand quadrant as shown inTable 3 below. TABLE 3 Walsh Code W0 W1 W2 W3 W4 W5 W6 W7 0 −1 −1 −1 −1−1 −1 −1 −1 1 1 1 −1 1 1 1 −1 1 2 −1 −1 1 1 −1 −1 1 1 3 −1 1 1 −1 −1 1 1−1 4 −1 −1 −1 −1 1 1 1 1 5 −1 1 −1 1 1 −1 1 −1 6 −1 −1 1 1 1 1 −1 −1 7−1 1 1 −1 1 −1 −1 1

[0017] Each Walsh code has a code length of 2^(n) bits, where n is apower of 2. In quadrature phase shift keying modulation, a Walsh code isrepresented by modulating the RF carrier phase between −90 degrees for a−1 and +90 degrees for a 1. Because −90 degrees and +90 degrees lie onthe real axis of a phase vector coordinate system, the correspondingcodes are called real codes.

[0018] In a code division multiple access system wherein orthogonalcodes are generated by Walsh functions, the user data rate may bevariable. For example, for a set of orthogonal Walsh codes having a codelength of eight and a basic data rate of R, a code division multipleaccess system can support the following scenarios:

[0019] (1) all eight users with a data rate of R,

[0020] (2) one user with a data rate of 2R and 4 users with a data rateof R,

[0021] (3) one user with a data rate of 4R and 2 users with a data rateof R, and

[0022] (4) one user with a data rate of 8R. In this case, the entirebandwidth is dedicated to a single user.

[0023] Other scenarios such as those described above may be used to showthat the number of available data rates for a given code length is halfthe code length. In the example above, there are four data rates (R, 2R,4R, and 8R).

[0024] By introducing additional phase values for modulating the phaseof the RF carrier, a set of orthogonal complex codes to representsymbols transferred across the user links 108 may be selected. Each ofthe orthogonal complex codes has a selected code length other than2^(n). for example, a selected orthogonal complex code may have a codelength of 4n. Because there are more values of 4n in a given numericalinterval than there are values of 2^(n), a set of orthogonal complexcodes may be selected to utilize a greater portion of a fixed bandwidththan may be possible with the optimum set of real codes having a codelength equal to the closest value of 2^(n) that does not exceed thenumber of antenna elements of the feeder link antenna array.

[0025] By way of example, a set of orthogonal complex codes of codelength 4n to represent symbols transferred across the user links 108 maybe generated from the following Kronecker tensor product:

C _(L×P) =A _(L)

W _(P)  (1)

[0026] wherein

[0027] C_(L×P) is a matrix of complex codes each having a code lengthequal to L×P,

[0028] L is a positive integer,

[0029] P equals 2^(n) and n equals a positive integer,

[0030] W_(P) is a Walsh code of code length P,

[0031] A_(L) is a coefficient matrix of elements a_(jk), where j=1 . . .L, k=1 . . . L, and

a _(jk) =e ^(j2n(j−1)(k−1)/L)  (2)

[0032] The optimum Walsh code rate is the highest power of two that isless than or equal to the ratio of bandwidth to symbol rate, orspreading code length. For example, the optimum Walsh code length for 12antenna elements is 2³, since the next higher Walsh code length of 2⁴exceeds the number of antenna elements. Because orthogonal complex codesgenerated, for example, by formula (1) may have a code length of 4n, aset of orthogonal complex codes having a code length greater than theoptimum Walsh code length may be generated to fully utilize all 12antenna elements. For 12 antenna elements, the following mixture of datarates is possible:

[0033] (1) all 12 users with a data rate of R,

[0034] (2) one user with a data rate of 3R and nine users with a datarate of R,

[0035] (3) one user with a data rate of 6R and six users with a datarate of R, and

[0036] (4) one user with a data rate of 12R. In this case, the entirebandwidth is dedicated to a single user.

[0037] By way of example, to generate a set of complex codes of codelength 12 using formula (1), let L=3 and P=4. The complex CDMA code isthen given by the following $\begin{matrix}{C_{3 \times 4} = \begin{bmatrix}{a_{11}W_{4}} & {a_{12}W_{4}} & {a_{13}W_{4}} \\{a_{21}W_{4}} & {a_{22}W_{4}} & {a_{23}W_{4}} \\{a_{31}W_{4}} & {a_{32}W_{4}} & {a_{33}W_{4}}\end{bmatrix}} & (3)\end{matrix}$

[0038] Numerically, C_(3×4) equals the matrix of orthogonal complexcodes illustrated in FIG. 2. Each column and corresponding row of thematrix of orthogonal complex codes illustrated in FIG. 2 is a complexcode that is orthogonal to each of the other complex codes.

[0039] For the example of a given bandwidth of 5 MHz and an availablefeeder link bandwidth of 500 MHz, the bandwidth utilization of the userlink in the code division multiple access communication system 100 maybe improved from {fraction (64/100)}=64 percent for the optimum set ofreal codes to {fraction (100/100)}=100 percent by implementing a set oforthogonal complex codes such as those generated in the example above aswell as other sets of orthogonal complex codes that may be generated forspecific applications. The increase in bandwidth utilization isgenerally available in those cases where a set of orthogonal complexcodes may be generated having a code length that is greater than theoptimum real code length and less than or equal to the number of antennaelements in the feeder link antenna array for a given user linkbandwidth and a given data bit rate. The greater code length of theselected set of orthogonal complex codes allows more user terminals 110to share the same service area, thereby reducing the number of serviceareas required and the corresponding total cost of support equipment. Incases where the ratio of the spectrum bandwidth to the symbol ratehappens to be equal or very close to 2^(n), real codes are preferable tocomplex codes. At other ratios, however, complex codes may be usedadvantageously to increase the capacity of a code division multipleaccess communications system.

[0040] Other modifications, variations, and arrangements of the presentinvention may be made in accordance with the above teachings other thanas specifically described to practice the invention within the spiritand scope of the following claims.

What is claimed is:
 1. A method of increasing utilization of feeder linkbandwidth for a code division multiple access communications systemcomprising the steps of: selecting a set of orthogonal complex codeseach having a code length that is greater than a code length of anoptimum real code and less than or equal to a number of antenna elementsof a feeder link; and transferring symbols via the feeder link to orfrom at least one of a corresponding plurality of user terminals whereinthe symbols are represented by a corresponding one of the set oforthogonal complex codes.
 2. The method of claim 1 wherein the set oforthogonal complex codes is generated from a Kronecker tensor productgiven by formula: C _(L×P) =A _(L)

W _(P) wherein C_(L×P) is a matrix of orthogonal complex codes whereineach of the orthogonal complex codes has a code length equal to L×P, Lis a positive integer, P equals 2 ^(n) where n equals a positiveinteger, W_(P) is a Walsh code matrix for a code length of P, A_(L) is amatrix of coefficients a_(jk) wherein j is a row index equal to 1 . . .L, k is a column index equal to 1 . . . L, and a _(jk) =e^(j2n(j−1)(k−1)/L).
 3. The system of claim 1 wherein the correspondingone of the set of orthogonal complex codes has a code length of
 12. 4.The system of claim 1 wherein the number of antenna elements is
 12. 5. Acode division multiple access communications system comprising: a basestation; a geo-stationary platform; a plurality of user terminals; andat least one feeder link coupled to the plurality of user terminals andto the geo-stationary platform for transferring symbols between thegeo-stationary platform and at least one of the plurality of userterminals wherein the symbols are represented by a corresponding one ofa set of orthogonal complex codes having a code length that is greaterthan a code length of an optimum real code and less than or equal to anumber of antenna elements in an antenna array of the feeder link. 6.The system of claim 5 wherein the set of orthogonal complex codes isgenerated from a Kronecker tensor product given by: C _(L×P) =A _(L)

W _(P) wherein C_(L×P) is a matrix of orthogonal complex codes whereinthe at least one of the orthogonal complex codes has a code length equalto L×P, L is a positive integer, P equals 2^(n) and n equals a positiveinteger, W_(P) is a Walsh code matrix for a code length of P, A_(L) is amatrix of coefficients a_(jk), where j is a row index equal to 1 . . .L, k is a column index equal to 1 . . . L, and a _(jk) =e^(j2n(j−1)(k−1)/L).
 7. The system of claim 5 wherein the at least one ofthe set of orthogonal complex codes has a code length of
 12. 8. Thesystem of claim 5 wherein the number of antenna elements is
 12. 9. Amethod of increasing utilization of feeder link bandwidth in a codedivision multiple access communications system comprising the steps of:selecting a number of antenna elements for an antenna array of a feederlink according to a given antenna array gain and beamwidth; andselecting a set of orthogonal complex codes each having a code lengththat is greater than a code length of an optimum real code and less thanor equal to the number of antenna elements.
 10. The method of claim 9further comprising the step of transferring symbols across a user linkto or from a user terminal wherein the symbols are represented by acorresponding one of the set of orthogonal complex codes.